Question 13: x(a-b)+ y(b-a) = x(a-b) - y(a-b) , by taking out the negative of (b-a)
= (x-y) (a-b) , using the grouping method
So the grouping method is basically, as follows:
If you're given a(c+d) + b(c+d) , it can be "grouped" (factorised is a better...
You can write a^4 + 4b^4 as:
a^4 + 4a^2b^2 + 4b^4 - 4a^2b^2 =
(a^2 + 2b^2)^2 - (2ab)^2 after completing the square and rearranging as a difference of two squares.
now using the difference of two squares, we can factorise it to:
(a^2 + 2b^2 + 2ab) (a^2 + 2b^2 - 2ab)
rearranging the terms...